Special types of matrices

Identity matrix

An identity matrix is a square matrix where values are equal to 1 on the diagonal of the matrix and 0 everywhere else. Mathematically, it can be shown as follows:

This would look like the following:

Here, .

The identity matrix gives the following nice property when multiplied with another matrix A:

Square diagonal matrix

A square diagonal matrix is a more general case of the identity matrix, where the values along the diagonal can take any value and the off-diagonal values are zeros:

Tensors

An n-dimensional matrix is called a tensor. In other words, a matrix with an arbitrary number of dimensions is called a tensor. For example, a four-dimensional tensor can be denoted as shown here:

Here, R is the real number space.